Refrigerators use input power to lift heat from a cold cooling load and reject heat to a warm heat sink. Refrigerators are hardware implementations of refrigeration cycles. Many different kinds of refrigeration cycles are used, depending on the application. For example, cryogenic refrigerators are refrigerators that provide cooling at cryogenic temperatures (which are typically defined as temperatures less than approximately 150 K), and cryogenic refrigerators typically use gas (often helium that remains single-phase) as the working fluid. Most space-based, long-life cryogenic refrigerators can be grouped into one of two categories, according to how the working fluid flows through the refrigerator: (1) DC-flow (direct-current, continuous, unidirectional flow) and (2) AC-flow (alternating-current, oscillating flow). DC-flow refrigerators include: Joule-Thomson coolers and Reverse-Brayton coolers. AC-flow refrigerators include Stirling coolers, Pulse-Tube coolers and Double-Cycle coolers. Double-Cycle coolers have two AC-flow sub-cycles (for example, Stirling or Pulse-Tube sub-cycles) that operate 180° out-of-phase (exactly out-of-phase). AC-flow refrigerators typically use regenerative heat exchangers (“regenerators”). As sub-cycles of Double-Cycle coolers, the regenerators of each of the sub-cycles are replaced by a recuperator, which transfers heat back and forth between the two sub-cycles.
The amount of cooling a refrigerators can achieve for a given amount of input power is limited by the Second Law of Thermodynamics. The maximum amount of cooling per unit of input power is the Carnot Coefficient of Performance (Carnot COP):
                              COP          CARNOT                =                                            Q              CX                                      W              I                                =                                    T              C                                                      T                H                            -                              T                C                                                                        (        1        )            where:                COPCARNOT=Carnot Coefficient of Performance, (no units);        Qcx=Maximum Amount of Cooling, Watts;        WI=Input Power, Watts;        TC=Temperature of the Cooling Load, K; and        TH=Temperature of the Heat Sink, K.The actual COP achieved by a refrigerator must always be less than the Carnot COP, according to the Second Law of Thermodynamics. The efficiency of a refrigerator is often expressed in terms of the percentage of the Carnot COP achieved by the refrigerator.        
It is important for space-based cryogenic refrigerators to have high efficiencies. For example, space-based cryogenic refrigerators typically have efficiencies in the range of 1% to 10%, depending on the temperature of the cooling load. Highly efficient refrigerators require little power input and reject little heat. The power input to a space-based cryogenic refrigerator typically comes from solar panels, and waste heat is typically rejected by radiators. Large power inputs require large and heavy solar panels, and large heat rejection requires large and heavy radiators. The solar panels and radiators must be launched into orbit, and launch costs are typically $10,000 per lb. Therefore, high efficiencies for space-based cryogenic refrigerators minimize launch costs.
A large source of inefficiency in cryogenic refrigerators is heat leakage from the warm parts of the refrigerators to the cold parts. The heat leakage typically is comprised of two main components: (1) heat flow due to heat exchanger ineffectivenesses and (2) heat conduction through the materials from which the parts are made. In addition to the refrigerator's cooling load (for example, cryogenically cooled infrared detectors), the heat leakage represents an additional cooling load that the refrigerator must cool. For example, if a cryogenic refrigerator could lift 2 W of heat at an efficiency of 10% if there were no heat leakage, and if 1 W of heat leakage is actually present, then the refrigerator can accommodate only 1 W of heat from an external cooling load, and its efficiency is actually only 5%.
Heat leakage is especially troublesome for cryogenic refrigerators that provide cooling at very cold temperatures (for example, 10 K with a heat-sink temperature of 300 K). Both components of heat leakage are proportional to temperature difference, so the large temperature difference between cold load temperatures and warm heat-sink temperatures causes large heat leakage. Also, it is very difficult thermodynamically to produce very cold cryogenic temperatures. This fact is evident by studying equation 1: for a given heat-sink temperature, the Carnot COPs of refrigerators with cold load temperatures are low. Cryocoolers with cold load temperatures produce little cooling and require large power inputs, and the cryocoolers have large flows of working fluid and large components. Therefore, large amounts of heat are carried to the cold components by the large flows of working fluid (due to heat exchanger ineffectivenesses) and conduction is large through the large components with large cross-sectional areas. The large heat leakage subtracts from the small amount of cooling to produce little net cooling and low efficiencies.
A solution that mitigates the effects of heat leakage is to interrupt the flow of heat from the warm end to the cold end at warm temperatures and provide refrigeration at the warm temperatures to partially compensate for the heat leakage. As equation 1 indicates, the Carnot COPs of refrigerators that cool at warm temperatures are higher than the Carnot COP of refrigerators that cool at colder temperatures. Therefore, it is possible to provide refrigeration at warm temperatures to partially compensate for the heat leakage with smaller amounts of power input than if the heat is allowed to leak to components at colder temperatures.
A refrigerator that provides cooling at multiple temperatures is called a multi-stage refrigerator (or cooler). In some multi-state refrigerators, some of the working fluid is diverted (from the main flow to the colder stage, or stages) to warm stages, where the working fluid is expanded to provide refrigeration. Multi-stage refrigerators exist, but none (to the author's knowledge) have been built in which the sole purpose of the warm refrigeration stages is to partially compensate for heat leakage to the cold components of the refrigerator.
A thermal storage unit (TSU) is an adjunct device that allows a refrigerator to achieve a transient operational load profile that would be unachievable otherwise. For example, typical space missions require relatively large amounts of cooling for short time intervals (for example, for 9 minutes), but only modest amounts of cooling for the rest of the cycle (for example, for 81 minutes). The average cooling (in Watts) is the heat lifted (in Joules) divided by the cycle period (in seconds). The average cooling for a typical space mission is relatively small, but the relatively large peak cooling requirement must be met to satisfy mission requirements. A way to meet the average cooling with a low-capacity cooler and meet the peak cooling requirement is to use a thermal storage unit (TSU). A TSU discharges (provides cooling) during short time intervals when the cooling requirement is relatively large, and the low-capacity cooler charges the TSU (removes heat from the TSU) during the rest of the cycle when the cooling requirement is relatively small.
Therefore, a need exists for a multi-stage refrigeration cycle whose intermediate stage(s) interrupt heat leakage from the warm end to the cold end of the cycle and provide(s) refrigeration to partially compensate for the heat leakage.